Journal article
Operads of genus zero curves and the grothendieck-teichmüller group
PB De Brito, G Horel, M Robertson
Geometry and Topology | GEOMETRY & TOPOLOGY PUBLICATIONS | Published : 2019
Abstract
We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichmüller group. Using a result of Drummond-Cole, we deduce that the Grothendieck-Teichmüller group acts nontrivially on M0,•+1, the operad of stable curves of genus zero. As a second application, we give an alternative proof that the framed little 2-disks operad is formal.
Grants
Awarded by Fundação para a Ciência e a Tecnologia
Funding Acknowledgements
We are grateful to the Hausdorff Institute of Mathematics for the excellent working conditions during the Junior Trimester in Topology. Boavida de Brito was supported by FCT through grant SFRH/BPD/99841/2014. We would also like to thank Benjamin Collas, Philip Hackney and Craig Westerland for helpful mathematical discussions and Rosona Eldred and David Gepner for comments on earlier drafts of this paper.